If you insist on limiting it to showing the latest 5 links, you're going to have to write a bit of code (that I'm not convinced is worth it). Possible approaches include:

Filtering the output of said Link Manager widget

Creating a custom post type called 'Sidebar Links' and then writing your own widget that displays the 5 latest

Creating a totally custom interface and storage mechanism from scratch (definitely not recommended)

Another options is using something like Options Framework (http://wordpress.org/plugins/options-framework/) to add some Theme Options. You could add Link 1, Link 2, Link 3, Link 4, and Link 5 as options. It's not an amazing user interface, but it's another quick way to accomplish basically what you're looking for.

I tried the link-manager, but it still has to be done via the dashboard and worst of all, there's nearly no options. I want to post news there from other sites and show the newest 5. link-manager means I have to manually set the order and it'll take far too long for anyone to add link, reorganise the posts, then save.
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CullyJul 3 '13 at 23:51

> "but it still has to be done via the dashboard" Your question specifically says you didn't want to let them to them to the Menus part of the dashboard - are you trying to keep them out of the entire dashboard?
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MadtownLemsJul 23 '13 at 17:30

No... well put it this way.. this way is very convuluted and is a lot more complicated than it should be. It's so useless, I didn't bother using it. I want a simple form I can give to people where they can submit news URLs. I am not giving them dashboard access, and I am not patient enough to spend 10 minutes messing with the menu's just to get 1 link up there. I wanted a simple form where you type a header + url and press submit. Instead, people seem to rely on plugins which are far too complicated and not simple.
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CullyJul 25 '13 at 0:32